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Compactness in fuzzy minimal spaces

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  • Alimohammady, M.
  • Roohi, M.

Abstract

The purpose of this paper is devoted to generalize the concept of fuzzy compactness. In fact we have introduce the concept of fuzzy (countably) compactness in fuzzy minimal spaces and some related basic results in these new setting are given. Further, some results of fuzzy compactness for fuzzy topological spaces are achieved. For example, it is shown that (X,M) is fuzzy m-compact if and only if every fuzzy m-open cover of it has a finite 0-partition. Furthermore, every fuzzy m−CII space is a fuzzy m-Lindelof space.

Suggested Citation

  • Alimohammady, M. & Roohi, M., 2006. "Compactness in fuzzy minimal spaces," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 906-912.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:4:p:906-912
    DOI: 10.1016/j.chaos.2005.08.043
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    References listed on IDEAS

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    1. Alimohammady, M. & Roohi, M., 2006. "Fuzzy Um-sets and fuzzy (U,m)-continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 20-25.
    2. M. N. Mukherjee & S. P. Sinha, 1991. "Fuzzy θ -closure operator on fuzzy topological spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-6, January.
    3. Alimohammady, M. & Roohi, M., 2006. "Fuzzy minimal structure and fuzzy minimal vector spaces," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 599-605.
    4. Caldas, M. & Jafari, S., 2005. "θ-Compact fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 229-232.
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    Cited by:

    1. Mursaleen, M. & Mohiuddine, S.A., 2009. "Nonlinear operators between intuitionistic fuzzy normed spaces and Fréchet derivative," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1010-1015.
    2. Mohiuddine, S.A. & Danish Lohani, Q.M., 2009. "On generalized statistical convergence in intuitionistic fuzzy normed space," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1731-1737.
    3. Alimohammady, M. & Roohi, M., 2007. "Separation of fuzzy sets in fuzzy minimal spaces," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 155-161.
    4. Mursaleen, M. & Mohiuddine, S.A., 2009. "Statistical convergence of double sequences in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2414-2421.
    5. Karakus, S. & Demirci, K. & Duman, O., 2008. "Statistical convergence on intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 763-769.

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